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Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.


Papers
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Patent
05 Jun 2001
TL;DR: In this paper, the authors present a system and method for product verification for use with products intended to be introduced into circulation and including machine readable product data, and comprising a product data storage means, at least one portable reading device for said machine-readable product data.
Abstract: The present invention provides for a system and method for product verification for use with products intended to be introduced into circulation and including machine readable product data, and comprising a product data storage means, at least one portable reading device for said machine readable product data, wherein the machine readable product data is applied to products and is arranged for inspection by the at least one portable reading device remotely from the product data storage means and at at least one point in the product circulation route, and wherein the at least one portable reading device is arranged to verify the authenticity of the machine readable product data and thereby verify the authenticity of the product itself.

116 citations

Journal ArticleDOI
TL;DR: In this article, the use of consumer products by 144 college students was studied to determine the effects that adding symbols to written warnings, subjects' familiarity with the product, and type of ha...
Abstract: The use of consumer products by 144 college students was studied to determine the effects that (a) adding symbols to written warnings, (b) subjects' familiarity with the product, and (c) type of ha...

116 citations

Journal ArticleDOI
TL;DR: The conformal bootstrap program for superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets was developed in this paper.
Abstract: In this long overdue second installment, we continue to develop the conformal bootstrap program for $\mathcal{N}=4$ superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets. We review analytic results for this correlator and make contact with the SCFT/chiral algebra correspondence of Beem et al. [Commun. Math. Phys. 336, 1359 (2015)]. We demonstrate that the constraints of unitarity and crossing symmetry require the central charge $c$ to be greater than or equal to $3/4$ in any interacting $\mathcal{N}=4$ SCFT. We apply numerical bootstrap methods to derive upper bounds on scaling dimensions and operator product expansion coefficients for several low-lying, unprotected operators as a function of the central charge. We interpret our bounds in the context of $\mathcal{N}=4$ super Yang-Mills theories, formulating a series of conjectures regarding the embedding of the conformal manifold---parametrized by the complexified gauge coupling---into the space of scaling dimensions and operator product expansion coefficients. Our conjectures assign a distinguished role to points on the conformal manifold that are self-dual under a subgroup of the $S$-duality group. This paper contains a more detailed exposition of a number of results previously reported in Beem et al. [Phys. Rev. Lett. 111, 071601 (2013)] in addition to new results.

116 citations

Journal ArticleDOI
TL;DR: The paper describes in detail the development of a step -based generic product modelling (GPM) system which has been designed and implemented according to the integrated resources of step and supports a complete product information structure and standard data format.
Abstract: Concurrent engineering has been recognized as a business philosophy and methodology for integrating all aspects of a product lifecycle into the stages of product design. It demands that, as product design decisions are made, they are immediately evaluated in terms of functionality, manufacturability, assemblability, maintainability and recyclability. This requires that the entire enterprise share a common product model at any stage of the product lifecycle. The paper describes in detail the development of a step -based generic product modelling (GPM) system which has been designed and implemented according to the integrated resources of step and supports a complete product information structure and standard data format. It can therefore be used to integrate a variety of manufacturing activities in a concurrent engineering environment. The GPM system consists of a generic product model, a product model database, a GPM/AutoSolid interface, a GPM/AutoCAD interface, and a user interface. The user can model products using built-in templates. Application systems can either be included in the GPM system, or interact with the GPM system through physical files in accordance with the step standard. Examples are included to illustrate the use of the system.

115 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20244
20239,015
202219,171
20212,013
20202,263